What drives antigenic drift in a single influenza season
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What drives antigenic drift in a single influenza season?. Maciej F. Boni Stanford University, Department of Biological Sciences Co-authors: Julia R. Gog, Viggo Andreasen, Marcus W. Feldman. DIMACS Workshop on the Epidemiology and Evolution of Influenza Rutgers University, January 26, 2006.

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What drives antigenic drift in a single influenza season
What drives antigenic drift in a single influenza season?

Maciej F. BoniStanford University, Department of Biological SciencesCo-authors: Julia R. Gog, Viggo Andreasen, Marcus W. Feldman

DIMACS Workshop on the Epidemiology and Evolution of Influenza

Rutgers University, January 26, 2006


Flu epidemics and antigenic drift

Strains have accumulated mutations. But how many?

epidemic strain

NOV

APR

Flu epidemics and antigenic drift

weekly illnesses/10,000 inhabitants (NL)

20

( focus will be on HA1 )

1996

1997

1998

de Jong et al (2000)


Ha1 polymorphism local datasets
HA1 polymorphism – local datasets

  • Coiras et al, Arch. Vir. (2001)

  • Schweiger et al, Med. Microbiol. Immunol. (2002)

  • Pyhälä et al, J. Med. Virol. (2004)

mean within-season distance = 2.8 aa (6nt)

max within-season distance = 8 aa (25nt)


Neutral epidemic model

Number of infections with epidemic-originating strain

Number of infections with a strain k mutations away

Neutral Epidemic Model



Strain frequencies are poisson distributed
Strain frequencies are Poisson-distributed

Frequency of strain k:

Mean number of mutations per virus moves forward in time

according to a “molecular clock.”


Modeling antigenic drift and immunity

you may have conferred immunity from a previous season to one of these strains.

Modeling antigenic drift and immunity

the epidemic-originating strain

-2

-1

0

1

2

3

4


Modeling antigenic drift and immunity1
Modeling antigenic drift and immunity one of these strains.

the epidemic-originating strain

-2

-1

0

1

2

3

4

Distance between immunizing strain and challenging strain determines level of cross-immunity.

We model this as an infectivity reduction and say it wanes exponentially with distance:


Non neutral model
Non-neutral model one of these strains.

  • Amino-acid replacements in influenza surface proteins confer a fitness benefit via increased transmissibility

  • Hosts have some immunity structure from vaccination or previous infections

    ( need both )


Keeping track of hosts

j+k one of these strains.is distance between immunizing and challenging (infecting) strain

Keeping track of hosts


Keeping track of variables

infectivity reduction by previous infection one of these strains.

with a strain j amino acids away

force of infection of strain k

total force of infection

Keeping track of variables


Equations
Equations one of these strains.


Equations1

total immunity in population one of these strains.

cross-immunity between strains mamino acids apart

Equations


Equations2

mean fitness of strain population: one of these strains.W

Equations

fitness of strain k


Population genetics

Fisher’s Fundamental Theorem one of these strains.

Population genetics

Define mean antigenic drift in virus population as:

This is the Price Equation, thus, the basic influenza population dynamics

can be viewed in a standard population genetic framework.


Under neutrality
Under neutrality one of these strains.


Takes 7 aa-changes to escape 50% immunity one of these strains.

I(t)


Define the excess antigenic drift as
Define the excess antigenic drift as: one of these strains.

How do you know when the epidemic ends?


I(t) one of these strains.



Partial correlations
Partial correlations one of these strains.

immunity :

immune-escape/mutation :


Partial correlations1
Partial correlations one of these strains.

immunity :

immune-escape/mutation :



Public health implications
Public health implications one of these strains.

  • Vaccination strategies: under-vaccination or imperfect vaccination may cause much excess antigenic drift.

  • Pandemic implications: need to consider the effects of vaccination during the 2nd year after a pandemic, and their effects on the 3rd year after a pandemic.


Thanks
Thanks one of these strains.

Viggo Andreasen

University of Roskile, Department of Mathematics and Physics

Julia Gog

Cambridge University, Department of Zoology

Marc Feldman

Stanford University, Department of Biological Sciences

Freddy Christiansen

University of Aarhus, Department of Biology

Mike Macpherson

Stanford University, Department of Biological Sciences

( and for funding to NIH grant GM28016, NSF, and Stanford University )


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